Problem: Simplify the following expression: $ y = \dfrac{-1}{7} - \dfrac{a - 5}{8} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{8}{8}$ $ \dfrac{-1}{7} \times \dfrac{8}{8} = \dfrac{-8}{56} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{a - 5}{8} \times \dfrac{7}{7} = \dfrac{7a - 35}{56} $ Therefore $ y = \dfrac{-8}{56} - \dfrac{7a - 35}{56} $ Now the expressions have the same denominator we can simply subtract the numerators: $y = \dfrac{-8 - (7a - 35) }{56} $ Distribute the negative sign: $y = \dfrac{-8 - 7a + 35}{56}$ $y = \dfrac{-7a + 27}{56}$